Rule: Q[17, 18]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $\frac{583401555}{32768}\cdot t^{17}-\frac{300540195}{4096}\cdot t^{15}+\frac{1017958725}{8192}\cdot t^{13}-\frac{456326325}{4096}\cdot t^{11}+\frac{929553625}{16384}\cdot t^9-\frac{66927861}{4096}\cdot t^7+\frac{20369349}{8192}\cdot t^5-\frac{692835}{4096}\cdot t^3+\frac{109395}{32768}\cdot t$
• $P_2$:
  $\frac{583401555}{32768}\cdot t^{35}-\frac{188721563625}{1212416}\cdot t^{33}+\frac{90700781076675}{145793024}\cdot t^{31}-\frac{332960713536718575}{221168017408}\cdot t^{29}+\frac{5632429461296045413775}{2287209052024832}\cdot t^{27}-\frac{121814343461138093197047}{42313367462459392}\cdot t^{25}+\frac{389020492535471856910380551175}{156878840908706393890816}\cdot t^{23}-\frac{64975872152340701297581328615925}{40631619795354956017721344}\cdot t^{21}+\frac{3170499143530562786086025633001773325}{4081864133675586125813434138624}\cdot t^{19}-\frac{93064713104804478154759113364828992228975}{328185958211650800101525918179508224}\cdot t^{17}+\frac{5207375289011816703294171102311036088525}{67567697278869282373843571389898752}\cdot t^{15}-\frac{147816228048051242414375185891093992675}{9652528182695611767691938769985536}\cdot t^{13}+\frac{401347208550972401956345536343725075}{185625541974915610917152668653568}\cdot t^{11}-\frac{77119235759767187412948006094632825}{371251083949831221834305337307136}\cdot t^9+\frac{1536003944961853580182386046557675}{120872445937154351294890109820928}\cdot t^7-\frac{25382117862389049403403206871019}{57115551376897111051431590354944}\cdot t^5+\frac{1668422886011357950594476828945}{228462205507588444205726361419776}\cdot t^3-\frac{743473288404057206638622158245}{20790060701190548422721098889199616}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.